PRODUCTIVITY
CHROME - Makes web surfing smooth, effortless. Bookmarks are easily synced between all three of my devices (Bionic, Nexus 7 tablet, and desktop computer)
DROPBOX - Best cloud storage app I've found yet. Simple, effective, easy-to-use interface. Makes editing and accessing documents an absolute breeze between my devices. My wife uses my account credentials on her laptop and Incredible 4G, so it's become our family's universal cloud storage.
EVERNOTE - Great cloud-based note-taking app. Again, love the synchronization across devices. Use this most for grocery shopping checklists.
GMAIL - Nuff said.
GOOGLE CALENDAR - Latest version allows for reliable syncing with Google's cloud servers, allowing calendar to always stay up-to-date. Widget sometimes takes a few minutes to reflect changes, but it's reliable overall.
QUICKOFFICE PRO (approx. $14.99) - While obviously not as fully featured as the official Microsoft Office suite, this is a more than capable Android alternative that can read/create files ranging from Office 97/2003 through 2010.
QUICKPIC - Best photo gallery app I've come across so far.
NEWS AND READING
AMAZON KINDLE - Kindle services without having to pay for a Kindle? No brainer right there!
POCKET - Fantastic app for saving articles for offline reading. UI is intuitive and easy on the eyes.
PRESS - More elegant and cleaner interface than stock Google Reader
ENTERTAINMENT
GOOGLE PLAY MUSIC - Didn't really care for it when it first launched, but Google has really streamlined this program. Works great when I want to access music I don't listen to often enough to waste SD card storage space on them. Only drawbacks are there's no way to view music by file folders and you can select "All Music (Cloud and Local Storage)" or "Local Storage Only" but there's no option to only view "Cloud Storage" (so that means I have to tag my Google cloud albums differently so I can recognize which music ISN'T on my phone.
JEWELS PRO - Best generic version of Bejeweled out there. Great time-killer!
SONGZA - Music Concierge service is extremely innovative and does a better job exposing users to new and different music than Pandora does (also has a lockscreen widget, which Pandora lacks)
SOUNDHOUND - Very reliable song ID service. Worth the couple dollars it costs to buy.
SHOPPING
AMAZON - While lacking in some features, this is a great mobile version of Amazon.com and allows for easy browsing, purchasing.
AMAZON MP3 - Simple UI allows easy browsing and purchasing of music from Amazon's MP3 store. The only thing I wish they would fix is, if you tilt your phone and cause the screen to shift to landscape or portrait, then playback of samples stops.
BEST BUY - Latest update brought a complete redesign of app, which works equally well as an online shopping tool and an in-store resource (e.g. scanning barcodes to access reviews, local store inventory, etc.)